N=30
epsilon=10**(-15)
i=0
xpp=1.0
xp=z=2.0
abserr=abs(z)
while i <= N and abserr >= epsilon*abs(z):
  z=xp-(xp**2-2)*(xp-xpp)/((xp**2-2)-(xpp**2-2))
  print i,z
  abserr=abs(z-xp)
  xpp=xp
  xp=z
  i=i+1